We know that monsters grow stronger when fellow heroes join the fight against the minions of Hell. I assume (but am not sure) because of the monster buffs it increases the number of unique/elite/champion monsters and with the added help I'm eager to seek them out for the better loot (and the Nephalem Valor bonus at end game). So, are unique/elite/champion monsters spawns deterministic? Are there places where I will always find one, or is it totally random?
Most enemy spawns are completely random.
The only types of special enemies that spawn deterministic are event bosses (events and sidequests with a "mini-boss" will always have one, although not necessarily always the same) and main-story quest-related monsters.
But since events themselves are randomized, in and of themselves they are not worth focusing on.
It is the case that some areas seem to have a higher density of elites and other high end mobs. Their spawns within an area are not deterministic per se, but if you clear the zone you will tend to find more in some areas than others. One particular area of note that fits this mold is the Vault of the Assassin in Act II.
Elite pack spawns are not exactly random.
The location of each elite pack is random, or at least is randomly selected from a fixed set of spawn points based upon the semi-randomized arrangement of geographic elements. However, the number of elite packs appears to be set based upon a range of values for the given region, with a minimum and maximum value to the range.
For example, The Keep Depths Level 3 in Act 3 will always have at least 1, and as many as 4 elite packs, no matter where they spawn. Similarly, Festering Woods in Act 1 will always have at least 3 elite packs, and as many as 4 (possibly 5, but I'm not certain if the 5 stacks of NV I occasionally get in that zone are sometimes exclusively from elite packs, or always include the single event that can spawn in the zone randomly).
This is similar to treasure goblins, and resplendant chests. Some zones have a chance to randomly spawn one or the other, or both (and a very few zones seem to have the chance to spawn 2 goblins or resplendant chests).
Some of these areas have very clear patterns, and there are a few places where you can always find an elite pack. However, the one dungeon in Act 1's Festering Woods that I mentioned is the only location I can think of where there is a guaranteed elite pack spawning in exactly the same location every single game, with the only random elements being where that dungeon entrance spawns, and what affixes that elite pack has.